SOLUTION: If A and B are independent events, P(A) = 0.35, and P(B) = 0.25, find the probabilities below. (Enter your answers to four decimal places.) (a) P(A ∩ B) (b) P(A &

Algebra ->  Probability-and-statistics -> SOLUTION: If A and B are independent events, P(A) = 0.35, and P(B) = 0.25, find the probabilities below. (Enter your answers to four decimal places.) (a) P(A ∩ B) (b) P(A &      Log On


   

Question 1028147: If A and B are independent events, P(A) = 0.35, and P(B) = 0.25, find the probabilities below. (Enter your answers to four decimal places.)

(a) P(A ∩ B)
(b) P(A ∪ B)
(c) P(A | B)
(d) P(Ac ∪ Bc)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(a) P(A ∩ B) = P(A)P(B) = 0.35*0.25 = 0.0875, since A,B are independent.
(b) P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.35+0.25-0.0875 = 0.5125, by the addition law.
(c) P(A | B) = P(A ∩ B)/P(B) = 0.0875/0.25 = 0.35
(d) P(Ac ∪ Bc) = P(Ac) + P(Bc) - P(Ac ∩ Bc) = P(Ac) + P(Bc) - P(Ac)P(Bc) = 1 - 0.35 + 1 - 0.25 - (1 - 0.35)(1 - 0.25) = 0.65 + 0.75 - 0.4875 = 0.9125, since if two events are independent then so are their complements.